Gaussian Process Model for Estimating Piecewise Continuous Regression
Functions
- URL: http://arxiv.org/abs/2104.06487v1
- Date: Tue, 13 Apr 2021 20:01:43 GMT
- Title: Gaussian Process Model for Estimating Piecewise Continuous Regression
Functions
- Authors: Chiwoo Park
- Abstract summary: Gaussian process (GP) model for estimating piecewise continuous regression functions.
New GP model seeks for a local GP estimate of an unknown piecewise continuous regression function at each test location.
- Score: 2.132096006921048
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: This paper presents a Gaussian process (GP) model for estimating piecewise
continuous regression functions. In scientific and engineering applications of
regression analysis, the underlying regression functions are piecewise
continuous in that data follow different continuous regression models for
different regions of the data with possible discontinuities between the
regions. However, many conventional GP regression approaches are not designed
for piecewise regression analysis. We propose a new GP modeling approach for
estimating an unknown piecewise continuous regression function. The new GP
model seeks for a local GP estimate of an unknown regression function at each
test location, using local data neighboring to the test location. To
accommodate the possibilities of the local data from different regions, the
local data is partitioned into two sides by a local linear boundary, and only
the local data belonging to the same side as the test location is used for the
regression estimate. This local split works very well when the input regions
are bounded by smooth boundaries, so the local linear approximation of the
smooth boundaries works well. We estimate the local linear boundary jointly
with the other hyperparameters of the GP model, using the maximum likelihood
approach. Its computation time is as low as the local GP's time. The superior
numerical performance of the proposed approach over the conventional GP
modeling approaches is shown using various simulated piecewise regression
functions.
Related papers
- Max-affine regression via first-order methods [7.12511675782289]
The max-affine model ubiquitously arises in applications in signal processing and statistics.
We present a non-asymptotic convergence analysis of gradient descent (GD) and mini-batch gradient descent (SGD) for max-affine regression.
arXiv Detail & Related papers (2023-08-15T23:46:44Z) - Kernel-based off-policy estimation without overlap: Instance optimality
beyond semiparametric efficiency [53.90687548731265]
We study optimal procedures for estimating a linear functional based on observational data.
For any convex and symmetric function class $mathcalF$, we derive a non-asymptotic local minimax bound on the mean-squared error.
arXiv Detail & Related papers (2023-01-16T02:57:37Z) - Adaptive LASSO estimation for functional hidden dynamic geostatistical
model [69.10717733870575]
We propose a novel model selection algorithm based on a penalized maximum likelihood estimator (PMLE) for functional hiddenstatistical models (f-HD)
The algorithm is based on iterative optimisation and uses an adaptive least absolute shrinkage and selector operator (GMSOLAS) penalty function, wherein the weights are obtained by the unpenalised f-HD maximum-likelihood estimators.
arXiv Detail & Related papers (2022-08-10T19:17:45Z) - Active Nearest Neighbor Regression Through Delaunay Refinement [79.93030583257597]
We introduce an algorithm for active function approximation based on nearest neighbor regression.
Our Active Nearest Neighbor Regressor (ANNR) relies on the Voronoi-Delaunay framework from computational geometry to subdivide the space into cells with constant estimated function value.
arXiv Detail & Related papers (2022-06-16T10:24:03Z) - Scalable mixed-domain Gaussian processes [0.0]
We derive a basis function approximation scheme for mixed-domain covariance functions.
The proposed approach is naturally applicable to Bayesian GP regression with arbitrary observation models.
We demonstrate the approach in a longitudinal data modelling context and show that it approximates the exact GP model accurately.
arXiv Detail & Related papers (2021-11-03T04:47:37Z) - Non-Gaussian Gaussian Processes for Few-Shot Regression [71.33730039795921]
We propose an invertible ODE-based mapping that operates on each component of the random variable vectors and shares the parameters across all of them.
NGGPs outperform the competing state-of-the-art approaches on a diversified set of benchmarks and applications.
arXiv Detail & Related papers (2021-10-26T10:45:25Z) - Piecewise Linear Regression via a Difference of Convex Functions [50.89452535187813]
We present a new piecewise linear regression methodology that utilizes fitting a difference of convex functions (DC functions) to the data.
We empirically validate the method, showing it to be practically implementable, and to have comparable performance to existing regression/classification methods on real-world datasets.
arXiv Detail & Related papers (2020-07-05T18:58:47Z) - SLEIPNIR: Deterministic and Provably Accurate Feature Expansion for
Gaussian Process Regression with Derivatives [86.01677297601624]
We propose a novel approach for scaling GP regression with derivatives based on quadrature Fourier features.
We prove deterministic, non-asymptotic and exponentially fast decaying error bounds which apply for both the approximated kernel as well as the approximated posterior.
arXiv Detail & Related papers (2020-03-05T14:33:20Z) - Robust Gaussian Process Regression with a Bias Model [0.6850683267295248]
Most existing approaches replace an outlier-prone Gaussian likelihood with a non-Gaussian likelihood induced from a heavy tail distribution.
The proposed approach models an outlier as a noisy and biased observation of an unknown regression function.
Conditioned on the bias estimates, the robust GP regression can be reduced to a standard GP regression problem.
arXiv Detail & Related papers (2020-01-14T06:21:51Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.